Astronomy & Celestial Mechanics
the sky, computed
Concept

Evaporation — where it appears

The steady loss of stars from a cluster whose velocity distribution has a tail above escape speed. The tail is repopulated by encounters on a relaxation time, so a cluster sheds about one per cent of its members per relaxation time and dissolves after a hundred of them.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

7 decades of relaxation time, and a Hubble time between them. Crossing time and two-body relaxation time for 5 self-gravitating systems, against the number of bodies in each. The lower marks are the crossing time R/σ, which spans 3 decades; the upper ones are t_relax ≈ 0.1N/ln N times it, which spans 8. The horizontal rule is a Hubble time, and the same expression puts these systems on opposite sides of it. Two of them relax — an open cluster and a globular cluster — so their stars have exchanged energy, their heavy stars have sunk, and their present structure is not the one they were born with. The rest do not: a dwarf spheroidal, an elliptical galaxy, a cluster of galaxies, the elliptical missing it by a factor of 10⁶, which is why a galaxy is modelled as a smooth potential with no stars in it at all. The dependence is on N and hardly at all on anything else, because the Coulomb logarithm makes every decade of impact parameter contribute equally. A cluster that relaxes also evaporates: about a stellar mass in a hundred and forty leaves per relaxation time, so the globular cluster empties in 6.1·10¹¹ years.

How long a system takes to forget

A star crossing a galaxy is deflected by every other star, and the deflections add as a random walk. The time for that walk to change a star's energy by its own amount is a hundred million billion years for a galaxy and a billion for a globular cluster, and everything about how the two are modelled follows from which side of a Hubble time that falls on.

gravitation · Two-body relaxation 7 decades of relaxation time, and a Hubble time between them. Crossing time and two-body relaxation time for 5 self-gravitating systems, against the number of bodies in each. The lower marks are the crossing time R/σ, which spans 3 decades; the upper ones are t_relax ≈ 0.1N/ln N times it, which spans 8. The horizontal rule is a Hubble time, and the same expression puts these systems on opposite sides of it. Two of them relax — an open cluster and a globular cluster — so their stars have exchanged energy, their heavy stars have sunk, and their present structure is not the one they were born with. The rest do not: a dwarf spheroidal, an elliptical galaxy, a cluster of galaxies, the elliptical missing it by a factor of 10⁶, which is why a galaxy is modelled as a smooth potential with no stars in it at all. The dependence is on N and hardly at all on anything else, because the Coulomb logarithm makes every decade of impact parameter contribute equally. A cluster that relaxes also evaporates: about a stellar mass in a hundred and forty leaves per relaxation time, so the globular cluster empties in 6.1·10¹¹ years.

A cluster that boils itself away

A star cluster has no thermostat. Encounters between its members push a few of them above escape speed, the cluster loses them, and losing them makes it contract — which makes it hotter, which makes more of them escape. A self-gravitating system heats up as it loses energy, and the process ends by destroying the system.

gravitation · Two-body relaxation

Named alongside it

The objects these essays reach for when they reach for this one.

Core collapseEquipartitionMass segregationRelaxation timeBinary heatingCluster dissolutionThe collisionless Boltzmann equationCollisionless systemCoulomb logarithmCrossing timeEscape velocityGlobular cluster

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